I would like to find the derivative of the quantity below w.r.t. $X:$
$\frac{\partial}{\partial X} \ln(|X|)$.
How could I use the following expression from: https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf ?
$∂(ln(det(X)))=Tr(X^{-1}∂X)$ eq. 43
Or if could I somehow transform it in such form so I can use eq.43? I am not looking for some fancy derivation, just an expression that can be easily implemented on R/Python/Matlab.
Essentially what the Eq. 43 expression works out to is that the derivative of $\ln(|X|)$ with respect to an element $X_{i,j}$ (that is, $\frac{\partial (\ln(|X|))}{\partial X_{i,j}}$) is just $(X^{-1})_{j,i}.$ Is that what you want to compute?